Cullen is 10 years younger than Ada. The product of their ages 2 years ago was 39.

) What is the difference between a sequence and a series? A sequence is an ordered list of numbers whereas a series is an unorde

vivado [14]

Answer:

a) A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers; b) A series is divergent if it is not convergent. A convergent series is a series for which lim n → ∞ an exists.

Step-by-step explanation:

A sequence is a pattern; it is an ordered list of numbers. A series, however, is the sum of a sequence.

A convergent series is a series for which the sequence of its partial sums tends to a limit; this means the limit exists. A divergent series is a series that is not convergent.

7 0

2 years ago

Consider the system: y = 3x + 5 y = ax + b What values for a and b make the system inconsistent? What values for a and b make th

AnnyKZ [126]

<span>When a = 3 and b ≠ 5, the system will be inconsistent because the lines will be parallel. When a = 3 and b = 5, the system will be consistent and dependent because they represent the same line.</span>

7 0

2 years ago

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If the function y = sinx is transformed to y = 3 sine (two-thirds x), how do the amplitude and period change?

icang [17]

Answer:

Amplitude increases and the period decreases

Step-by-step explanation:

Here, we are to compare amplitude change and period change

The first equation is;

y = sin x

The second is

y = 3 sine (2/3)x

Generally, the equation of a sine graph can be written as;

y = a sin (bx + c)

where a represents the amplitude and b refers to the period

In the first equation , a = 1 while in the second , a = 3 ; This shows an amplitude increase

In the first equation, b = 1 while in the second equation b = 2/3; this shows a period decrease

7 0

2 years ago

Read 2 more answers

The average life of a bread-making machine is 7 years, with a standard deviation of 1 year. Assuming that the lives of these mac

Alina [70]

Answer:

a) $P(6.4$

b) $a=7 +1.036*0.333=7.345$

So the value of bread-making machine that separates the bottom 85% of data from the top 15% is 7.345.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Let X the random variable life of a bread making machine. We know from the problem that the distribution for the random variable X is given by:

$X\sim N(\mu =7,\sigma =1)$

We take a sample of n=9 . That represent the sample size.

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is also normal and is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\bar X \sim N(\mu=7, \frac{1}{\sqrt{9}})$

Solution to the problem

Part a

(a) the probability that the mean life of a random sample of 9 such machines falls between 6.4 and 7.2

In order to answer this question we can use the z score in order to find the probabilities, the formula given by:

$z=\frac{\bar X- \mu}{\frac{\sigma}{\sqrt{n}}}$

The standard error is given by this formula:

$Se=\frac{\sigma}{\sqrt{n}}=\frac{1}{\sqrt{9}}=0.333$

We want this probability:

$P(6.4$

Part b

b) The value of x to the right of which 15% of the means computed from random samples of size 9 would fall.

For this part we want to find a value a, such that we satisfy this condition:

$P(\bar X>a)=0.15$ (a)

$P(\bar X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.85 of the area on the left and 0.15 of the area on the right it's z=1.036. On this case P(Z<1.036)=0.85 and P(Z>1.036)=0.15

If we use condition (b) from previous we have this:

$P(X$